The Bersa Thunder .380 should have a rear sight that is adjustable for 'windage' (side to side movement). All you need is a small screwdriver &, perhaps, a couple of boxes of ammo to test with as you're adjusting.

Once you have the gun 'zeroed' where you want it, be sure & apply a small amount of 'lock-tite' to the adjustment screw so that it won't allow the sights to become 'out of zero' again as you shoot.

There's not really anything you can do about 'elevation' (up & down movement) with your sights except, perhaps, to aim higher.

"Trying to win hearts & minds, but willing to splatter them if necessary"

Your Bersa is not shooting low and to the left...you are. This is very common, and not specific to Bersas. You need to work on your grip and trigger pull and try loading some snap caps in your mag along with your live ammo and see what happens when you drop the hammer on a snap cap. You'll see your front sight take a dive.